In Visio 2013 (in fact in many of the Office applications), we can simulate this effect by using the “Soft Edges” feature. Below is an example of what could be done in Visio.

The technique is very simple, for any shape – I'll get to the limitations later – simply apply a varying amount of Soft Edges.

First, draw a simple shape with a solid fill color, right-click on the shape and select Shape Format.

And then under Format Shape, select the Effects icon (the pentagon) and then soft edges

They key is to vary the Size value.

Below are some examples of how size effects the shape. The first shape has no Soft Edges applied, the 2nd has the Soft Edge size set to 12pt, and then the 3rd set to 24pt. Notice that the Soft Edges effect diminishes the apparent size of the shape. Compare no soft edge with 12 pt and 24 pt soft edge.

Keep in mind that “soft edges” is not the same blur. It won't affect the internal components of a shape. This is easy to demonstrate if you apply Soft Edges to a bitmap. Notice that as the edge gets more blurred, the internal contents are not changed.

Soft Edges also affects grouped shapes by softening each individual component shape and not the edge of the group.